I want to compare 2 models (a lagged and simultaneous version). However, due to having ordinal data I cannot do the usual chi-square difference testing (I get the warning message: The chi-square value for MLM, MLMV, MLR, ULSMV, WLSM and WLSMV cannot be used for chi-square difference tests).

You can do chi-square difference testing for these estimators but not in the conventional way. For the estimators that end in MV, you can use the DIFFTEST option of the SAVEDATA and ANALYSIS commands to do this. For the other estimators listed, see Chi-Square Difference Test For MLM and MLR in the left column of the website.